Quantitative trait locus (QTL) studies of a skeletal trait or a few related skeletal components are becoming commonplace, but as yet there has been no investigation of pleiotropic patterns throughout the skeleton. We present a comprehensive survey of pleiotropic patterns affecting mouse skeletal morphology in an intercross of LG/J and SM/J inbred strains (N = 1040), using QTL analysis on 70 skeletal traits. We identify 798 single-trait QTL, coalescing to 105 loci that affect on average 7–8 traits each. The number of traits affected per locus ranges from only 1 trait to 30 traits. Individual traits average 11 QTL each, ranging from 4 to 20. Skeletal traits are affected by many, small-effect loci. Significant additive genotypic values average 0.23 standard deviation (SD) units. Fifty percent of loci show codominance with heterozygotes having intermediate phenotypic values. When dominance does occur, the LG/J allele tends to be dominant to the SM/J allele (30% vs. 8%). Over- and underdominance are relatively rare (12%). Approximately one-fifth of QTL are sex specific, including many for pelvic traits. Evaluating the pleiotropic relationships of skeletal traits is important in understanding the role of genetic variation in the growth and development of the skeleton.

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THE skeleton is a complex system composed of functionally interacting parts, with a variety of developmental histories. Knowledge of the genetic architecture of the skeleton is important in exploring questions about the evolution of the system as a whole in vertebrates as well as in biomedical research on the genetics of bone growth and disease. Aspects of genetic architecture include number and size of gene effects, dominance interactions within loci, epistatic interactions among loci, and pleiotropic patterns.

Studies of the genetic architecture of components of body size are becoming more and more common (CHEVERUD et al. 2001; LEAMY et al. 2002; CHRISTIANS et al. 2003; LIONIKAS et al. 2003; BROCKMANN et al. 2004; ROCHA et al. 2004). Among components of body size, there are now many published articles on the genetic architecture of skeletal traits and aspects of skeletal morphology using quantitative trait locus (QTL) analysis (CHEVERUD et al. 1997, 2001; LEAMY et al. 1999; KLEIN et al. 2001; KLINGENBERG et al. 2001; CHASE et al. 2002; LI et al. 2002; SHIMIZU et al. 2002; CHRISTIANS et al. 2003; VOLKMAN et al. 2003; BOUXSEIN et al. 2004; HUANG et al. 2004; ALAM et al. 2005; CARRIER et al. 2005; LANG et al. 2005; ISHIMORI et al. 2006; KENNEY-HUNT et al. 2006; WOLF et al. 2006; CHRISTIANS and SENGER 2007; FARBER and MEDRANO 2007; YU et al. 2007; ZHOU et al. 2007). These studies are usually limited to a single trait or a few traits of interest, such as bone mineral density, or to a specific region of the skeleton, such as the innominate or mandible. While most loci are thought to be pleiotropic, having effects on two or more traits (WRIGHT 1980), very few studies have measured enough traits to make an overall analysis of pleiotropic patterns in QTL meaningful. Here we present the results of a search for QTL with effects on 70 traits throughout the mouse skeleton and the pleiotropic relationships among those single-trait QTL. To the best of our knowledge, this is the most comprehensive study of the genetic architecture of the skeleton to date.

The LG/J x SM/J intercross:

The experimental population results from an intercross of inbred mouse strains LG/J and SM/J (CHEVERUD et al. 1996, 2001; VAUGHN et al. 1999). LG/J and SM/J were selected for large and small body weight at 60 days of age, respectively (GOODALE 1938; MACARTHUR 1949), and have been inbred for >100 generations. LG/J and SM/J adult weight differed by >20 grams on average (CHAI 1956a,b, 1957) in the 1950s, but SM/J has increased slightly in size since then (KRAMER et al. 1998). CHEVERUD and COLLEAGUES (1996) crossed 10 LG/J females to 10 SM/J males in 1991. The F₁ generation was intercrossed to produce the F₂ generation (intercross I, n = 533). The LG/J x SM/J intercross was replicated in 1995 (intercross II, n = 507) (CHEVERUD et al. 2001). Intercrosses I and II are combined in this study for a total of 1040 F₂ mice.

Animals were weaned at 21 days of age and housed in single-sex cages of no more than five animals per cage, except for breeding mice (intercross II only), which were housed in breeding pairs. The breeding mice were selected randomly from intercross II individuals to form an advanced intercross line (AIL) (EHRICH et al. 2005) and a panel of recombinant inbred lines (RILs) (KRAMER et al. 1998; CHEVERUD et al. 1999; HRBEK et al. 2006). Standard mouse chow, an irradiated diet of 20% protein and 4.5% fat [Purina (St. Louis) PicoLab Rodent Chow 20 (5353)], was fed to the animals ad libitum postweaning. The mice were weighed weekly for 10 weeks. At promptly 10 weeks of age in intercross I and at variable times after 10 weeks in intercross II, the animals were killed by CO₂ asphyxiation and necropsied. The ages at necropsy in intercross II range between 72 and 237 days with a mean of 144 days (KENNEY-HUNT et al. 2006).

Genotypes:

DNA was extracted from the spleens of intercross I animals and from the livers of intercross II animals. DNA extraction and PCR amplification protocols are outlined in ROUTMAN and CHEVERUD (1995). Intercross I was scored for 76 microsatellite markers on all 19 autosomes in 55 intervals (CHEVERUD et al. 1996). Intercross II was scored for 95 markers in 71 intervals (VAUGHN et al. 1999). The X chromosome was not genotyped with microsatellites in either intercross. Intercross II was also genotyped commercially for 369 single-nucleotide polymorphisms (SNPs), including 16 SNPs on the X chromosome, using the GoldenGate assay (Illumina, San Diego). Supplemental Appendix A lists the markers and their locations in the physical and genetic maps. Marker order was established using physical positions obtained from the Ensembl database (http://www.ensembl.org) or from Illumina and verified in R/qtl (BROMAN et al. 2003). Haldane's map distances were computed using R/qtl (BROMAN et al. 2003). The combined map distance of all chromosomes was 1796 cM, with an average of 3.98 cM between the 471 markers. The largest intermarker distances were 17.1 cM on chromosome 14 and 14.5 cM on chromosome 8. These regions lacked any detectable SNP variation between LG/J and SM/J despite being scored for >30 SNPs known to be polymorphic between inbred mouse strains (HRBEK et al. 2006). In previously published work in this experimental population, for which only microsatellite genotypes were available, the average intermarker distance was 23 cM (VAUGHN et al. 1999; KENNEY-HUNT et al. 2006).

Phenotypes:

Body weights were collected at necropsy to the nearest hundredth of a gram, using a digital balance. Tail length measurements were collected at necropsy in intercross II, using digital calipers to the nearest hundredth of a millimeter. Carcasses were frozen immediately after necropsy and then later skinned and dried. Dermestid beetles were used to deflesh the carcasses. Femur, tibia, humerus, and ulna lengths were measured using digital calipers, to the nearest hundredth of a millimeter. Mandible landmarks were recorded by a camera attached to a dissection microscope in intercross I (CHEVERUD et al. 1997) and scanned using a UMAX scanner in intercross II (EHRICH et al. 2003). Any differences in measurement between intercross I and II mandibles due to the different procedures followed was accounted for by removing these effects from the data prior to mapping analysis (see below). Twenty-five digital images were obtained of 15 different bones from each individual, using a Nikon Coolpix 4500 digital camera with an effective resolution of 4.0 megapixels attached to a minitripod of fixed height. Skeletal measurements on the cranium, scapula, innominate, sacrum, vertebrae, and foot were obtained to the nearest hundredth of a millimeter from the digital images, using Scion (Frederick, MD) Image software. Traits on the cranium, mandible, scapula, innominate, sacrum, vertebrae, and foot are shown in Figure 1. All measurements were taken on the animal's right side (where applicable), unless a missing or damaged specimen required the measurement to be taken on the left. Table 1 describes the 70 traits included in the study. Vertebral traits 1, 2, 3, and C were measured on the cranial surface of the third thoracic, first lumbar, and fourth lumbar vertebrae and on the caudal surface of the eighth thoracic and third caudal vertebrae. The differences in which surfaces were measured were due to different curvatures in the shape of those vertebrae. All measurements were highly repeatable as determined by the intraclass correlation of repeated measures (r² > 0.82 for all traits, mean r² = 0.93). Cranial traits vault height and face height, foot traits third metatarsal length and calcaneus length, all vertebral traits on the third thoracic vertebra, eighth thoracic vertebra, and third caudal vertebra, and the lengths of the first and fourth lumbar vertebrae were triple measured to ensure that repeatability of the average was >90%. All 7 mandible traits were initially measured as areas (in square millimeters). Their square roots (in millimeters) were used in the quantitative genetic analysis so that the dimensions of all traits would be the same. This had no effect on the identification of QTL.

View larger version (16K): In this window In a new window Download PPT slide   FIGURE 1.— Skeletal traits included in the study. (A–C) Cranial traits. (D) Mandible traits. (E) Innominate traits. (F) Vertebral traits, coded V#XN, where "#" is vertebral number, "X" is type (thoracic, lumbar, or caudal), and "N" is trait (1, 2, 3, C, or L, shown). (G) Foot traits. (H) Sacral traits. (I) Scapular traits. Not shown: body weights, tail length, long bone lengths. Figure after Anatomy of the Laboratory Mouse (COOK 1965).

 

View this table: In this window In a new window   TABLE 1 Skeletal traits

 
Before analysis, extreme outliers were removed from the data set to avoid biasing the data. Next, the effects of dam, litter size, experimental block, and sex were removed as in CHEVERUD et al. (1996) to reduce nongenetic variance and thus to increase the ability to detect QTL. Effects were removed by adding the difference between the overall trait mean and the class mean for that trait to each animal's trait value, by class in a serial fashion. Litter size was divided into two classes, litter size of 10 and litter size >10. Experimental block was based on date of birth, as animals were born at roughly monthly intervals. Experimental block corrected for any change in the environment over time and any change in measurement practices over time, as mice were measured in birth order. Sex effects must be removed because mice are sexually dimorphic for body weight and for most skeletal traits. The effects of age at necropsy were removed from intercross II individuals by multiplying the residuals from a linear regression by the value (necropsy age, 72 days) and subtracting that result from the trait value. Finally, the effect of intercross was removed and the intercrosses were combined. All QTL analysis was performed on the combined and corrected data set.

Analysis:

On the autosomes, QTL map positions and effects were calculated using interval mapping as described by HALEY and KNOTT (1992) and VAUGHN et al. (1999). Marker positions were assigned the additive genotypic scores –1 (SM/J homozygotes), 0 (heterozygotes), and +1 (LG/J homozygotes) and the dominance genotypic scores 1 (heterozygotes) and 0 (both homozygotes). Genotypes were imputed every 1 cM along each chromosome, using the genotypic scores of the flanking markers and the recombination rate (HALEY and KNOTT 1992). The SETCOR function in SYSTAT 10.2 (Systat Software, San Jose, CA) was used to regress trait values onto the additive and dominance genotypic scores at each marker and imputed position and to obtain F- and ²-statistics for the individual traits under a null hypothesis of no gene effect. QTL positions were determined by the site with the least probability (p) of the genotype–phenotype correlation occurring by chance. The likelihood probability ratio (LPR) score of a QTL is –log₁₀(p). Thus, the higher the LPR, the more confidence a QTL exists at that location.

Chromosomewide and genomewide significance levels were calculated using the effective marker number (M_eff),

where M is the number of markers that were scored, and V is the variance of the eigenvalues of the intermarker correlation matrix for each chromosome (CHEVERUD 2000). The Bonferroni-corrected 5% chromosomewide significance threshold is calculated by dividing 0.05 by M_eff for that chromosome. The genomewide threshold is calculated by dividing 0.05 by the sum of M_eff over all chromosomes. Chromosome-specific thresholds are given next to the chromosome name in supplemental Appendix C. The use of chromosomewide thresholds for gene mapping is recommended by CHEN and STOREY (2006) as an appropriate balance to limit false positive significant results while still retaining as many true positives as possible. The genomewide significance threshold over the autosomes is 3.95.

The X chromosome is a special case and must be analyzed differently. In the F₂ generation of this intercross, males can be hemizygous LG/J or SM/J. There is never any dominance in males because they have only one X chromosome. Females can either be homozygous LG/J or heterozygous. There are no female SM/J homozygotes at any loci on the X chromosome in the F₂ generation due to the breeding scheme, in which two LG/J X chromosomes (P₁ dams) but only one SM/J X chromosome (P₁ sires) were included in the original cross. The QTL analysis on the X chromosome was performed in R/qtl 1.05 (BROMAN et al. 2003), to avoid false linkage caused by sex differences (BROMAN et al. 2006). BROMAN et al. (2006) described how to determine significance thresholds on the X chromosome using R/qtl. Here 8000 permutations were used to find the X chromosome-specific threshold.

Each single-trait QTL was examined for sex specificity by regressing the phenotype on the additive- and dominance-by-sex interaction terms, controlling for the main effects of sex and the additive and dominance genotype scores. A significant sex-by-QTL interaction at the 5% level indicates that the QTL effects are sex specific. Functionally, our test is the same as the one performed by SOLBERG et al. (2004), but using a least-squares fit rather than maximum likelihood. This test for sex specificity is considered protected from multiple comparisons because the location was previously identified on the basis of its pooled-sex effect. Given a significant sex-by-genotype interaction, separate analyses were performed in the two sexes. The significance thresholds for single-sex QTL were roughly equivalent to the thresholds for combined-sex QTL. Two-QTL tests were also performed to test the model of two QTL for a single trait on one chromosome. If the data fit a two-QTL model better than a single-QTL model at the 5% level (HALEY and KNOTT 1992), two QTL for the trait were located on the chromosome. Next, formal tests for pleiotropy were performed, using the multivariate tests for pleiotropy proposed by KNOTT and HALEY (2000) and described by EHRICH et al. (2003). Residuals were obtained for each trait at its most likely location and then the residuals were combined into a single residual sums-of-squares and cross-products (SSCP) matrix assuming each trait maps to its own location. At the most likely location of the combined traits, a residual SSCP matrix was calculated assuming the traits map to the same pleiotropic locus. The SSCP matrices were compared using the equation

where d.f. is the residual degrees of freedom based on the number of individuals, SSCP_l is from the model assuming individual linked locations, and SSCP_p is from the pleiotropic model (KNOTT and HALEY 2000). Pleiotropy was the null hypothesis. The separate locus model was accepted if the probability of the ²-test was 0.05. Traits were added to the pleiotropy model one chromosomal position at a time on the basis of proximity. For example, the two most closely located QTL on a chromosome were tested for pleiotropy, and, if positive, the pleiotropic QTL was placed at the location for the combined traits. Then the next two closest QTL were tested for pleiotropy, and so on. On the X chromosome, tests for pleiotropy were performed using only females, to avoid the problem with false linkage mentioned above.

To test for similarity between phenotypic correlations (supplemental Appendix B) and patterns of pleiotropy, a matrix of pleiotropic scores was constructed (supplemental Appendix E). Each pair of traits was scored for the number of times the traits co-occurred in a locus. To achieve the pleiotropic score, this value was divided by the sum of the number of single-trait QTL for the trait pair divided by two. In this way, if there were 10 single-trait QTL for each trait in the trait pair, and they co-occurred five times, the pleiotropic score was 0.5. A Mantel test (MANTEL 1967) was performed to test the similarity of the matrix of pleiotropic scores with the phenotypic correlation matrix. This test was performed using the "mantel" function of the "vegan" package (http://cran.r-project.org/web/packages/vegan/index.html) in the statistical software R, using 50,000 permutations. The null hypothesis is that there is no association between the matrices.

Basic statistics:

Standard deviations, means, and sample sizes of all traits, after correction for the effects of dam, litter size, experimental block, necropsy age, sex, and intercross, are shown in Table 2. Mice are highly sexually dimorphic in body weight with males larger than females, and this is true for most skeletal traits as well. The exceptions were five of the eight innominate traits, the lengths of the first and fourth lumbar vertebrae, sacroiliac joint length, and three of the seven mandibular traits that were larger in females than in males. Seven traits were found to have no difference in size between the sexes. These traits were iliac crest length (another innominate trait), the centrum heights of the eighth thoracic, first lumbar, and fourth lumbar vertebrae, and three mandibular traits. The matrix of phenotypic correlations is shown in supplemental Appendix B.

View this table: In this window In a new window   TABLE 2 Basic statistics of the traits

 

Individual-trait QTL:

QTL analysis of the effects on the 70 traits resulted in 798 individual-trait QTL (supplemental Appendixes C and D). Of these, 14% were specific to males and 8% were specific to females. A possible influence on the higher number of male QTL is that males were larger than females in nearly every trait and thus had a higher variance. Fifty-nine percent of the individual-trait QTL exceeded the genomewide 5% significance threshold of 3.95. The mean LPR was 5.76, with the scapula length trait on chromosome 6 having the highest LPR (28.29). Confidence intervals, according to convention, were defined as the region with LPRs within one of the peak LPR. The mean confidence interval was 19.6 cM, with a range from 2 to 59 cM. In 65 cases there were 2 QTL for one trait on the same chromosome. Eighteen (28%) of these were on chromosome 6. The average number of QTL per trait was 11, with a minimum of 4 (three caudal vertebra traits) and a maximum of 20 (innominate length).

Results for additive (a) and dominance (d) genotypic values are compared for the autosomes only. At most of the 792 autosomal single-trait QTL the LG/J allele resulted in a larger skeletal element. A negative additive genotypic value, indicating that the SM/J allele leads to larger size, occurred in only 11% of QTL. Negative additive genotypic values tended to be concentrated on specific chromosomes. For example, 42% of the QTL on chromosome 5, 71% of the QTL on chromosome 18, and 38% of the QTL on chromosome 19 had negative additive genotypic values. Using the absolute value of a to compare the magnitude of effects, the mean standardized absolute additive genotypic value (|a|/SD) was 0.23 and the median was 0.22. As in KENNEY-HUNT et al. (2006), skeletal traits met quantitative genetic expectations of having mostly small (<0.20–0.30) standardized additive genotypic values. The largest a/SD value was 0.55, belonging to the scapula-length QTL on chromosome 6 that also has the highest overall LPR score.

To examine dominance relationships, the dominance genotypic value d is standardized by dividing it by the additive genotypic value a. It is useful to divide these ratios (d/a) into broader categories (KENNEY-HUNT et al. 2006). Strongly underdominant QTL were defined as those with d/a ratios < –2.5. Only 1% of QTL fell in this category, with the most underdominant being the anterior interorbital width (FCW) locus on chromosome 15 (d/a = –37.62). Underdominant QTL (2% of loci) had d/a ratios between –1.5 and –2.5. Eight percent of loci had d/a ratios between –1.5 and –0.5, in which SM/J was considered dominant to LG/J. A locus that is exactly codominant has a d/a ratio of 0. Here, a locus was considered to be codominant if the d/a ratio was between –0.5 and 0.5. Fifty percent of all QTL were codominant. With the exception of codominance, LG/J dominant to SM/J (0.5 < d/a < 1.5) was the most common dominance relationship in the study. Thirty percent of the loci had this relationship. LG/J overdominance (1.5 < d/a < 2.5) occurs in 5% of loci. The last category of dominance relationships, which occurred in 4% of loci, was strong overdominance, which included those with dominance ratios >2.5. The greatest d/a ratio, 2115, belonged to the femur-length locus on chromosome 19. The ulna-length QTL on the same chromosome was also strongly overdominant, with a d/a ratio of 26.64.

Pleiotropic loci:

Formal tests for pleiotropy resulted in 105 pleiotropic loci (Table 3 and Figure 2). The mean pleiotropic LPR was 10.10, a substantial increase from the mean of 5.76 for individual-trait QTL. The highest LPR was 28.64 (locus Skl3.04). Eighty-eight of the loci (84%) had LPRs >4.00, and 10 loci (9.5%) had LPRs >20. The confidence intervals ranged from 3 to 50 cM, with a mean confidence interval of 13.36 cM, smaller than the mean confidence interval for individual-trait QTL. The mean number of traits per locus was 7.6. Seventy percent of these pleiotropic loci had a sex-specific effect on at least one trait. The mean percentage of traits in a locus that were sex specific was 28%, but among those loci that had at least one sex-specific trait, the percentage of sex-specific traits increased to 40%. The greatest number of sex-specific traits occurred at locus Skl15.04, at which 8 of the 10 traits were specific to males only. Of the 73 loci with sex-specific effects, 19% of them had both male-only and female-only trait QTL while the remainder (81%) had effects restricted to either males or females. We also find that the matrix of pleiotropic scores and the phenotypic correlation matrix are strongly correlated (P < 2 x 10^–5, Mantel statistic r = 0.52). This suggests that pleiotropic patterns are predictable from phenotypic correlations.

View this table: In this window In a new window   TABLE 3 Pleiotropic loci

 

View larger version (20K): In this window In a new window Download PPT slide   FIGURE 2.— Map of pleiotropic loci. Lengths of chromosomes are shown at the bottom. Bars indicate confidence intervals. The pleiotropic locus name is located at the position of maximum LPR for the locus.

 
While only 11% of single-trait QTL had negative additive genotypic values, 37% of the pleiotropic loci affected at least one trait with a negative additive genotypic value. Antagonistic pleiotropy with respect to skeletal size, in which some traits at a locus are positively pleiotropic and some are negatively pleiotropic, is expressed in quantitative genetic terms as a locus at which one or more traits have a negative additive genotypic value (–a) and one or more traits have a positive additive genotypic value (+a). Here, a locus is considered to have antagonistic pleiotropy when >25% of traits at a locus have significant (P 0.05) negative a values and >25% have significant (P 0.05) positive a values. Antagonistic pleiotropy can be assessed for 92 of the pleiotropic loci, as it can be calculated only for autosomal QTL with two or more traits. Of the 34 pleiotropic loci that included traits with both positive and negative additive genotypic values, 41% exhibited antagonistic pleiotropy.

While mean LPRs and confidence intervals of individual-trait QTL were similar to those of the microsatellite-only mapping studies in the same population (VAUGHN et al. 1999; CHEVERUD et al. 2001; KENNEY-HUNT et al. 2006), the ability to detect two QTL for the same trait on the same chromosome was greatly improved by the increased marker density achieved through genotyping intercross II for SNPs. For example, KENNEY-HUNT et al. (2006) included long bone lengths and necropsy weights for the same population of animals but used only the microsatellite markers, which had an average intermarker distance of 23 cM. In that study only one instance of two QTL on the same chromosome was detected for necropsy weight or any of the four long bone lengths (two necropsy weight QTL on chromosome 6). With the new SNP marker genotypes, nine more instances of two-QTL chromosomes were identified for these five traits. Femur length gained a second QTL on chromosomes 4 and 13, humerus length gained a second QTL on chromosomes 1 and 13, tibia length gained a second QTL on chromosomes 1, 4, and 13, and ulna length gained a second QTL on chromosomes 1 and 6.

A very high number of single-trait QTL were identified and many were strongly significant. While many of the measurements were of small skeletal traits, in the 1- to 2-mm range, at least four QTL were identified for every trait included in the study. Dominance, including over- and underdominance, was present at 50% of loci, and, where present, the LG/J allele was most often dominant to the SM/J allele. When SM/J was dominant to LG/J, in about one-third of loci the SM/J allele also resulted in a larger size. Overall 22% of QTL were specific to males or females, but three innominate traits were sex specific at 50% of their QTL, innominate length, ilium length, and pubis length. This suggests the possibility of different genetic systems for the male and the female pelvis, especially given that morphology in this region of the skeleton has an impact on reproduction.

About 20% of the loci having sex-specific effects had both male- and female-specific effects on different traits at the same QTL. It is possible that these effects are actually due to separate loci too closely linked to be detected separately in an F₂ population, one locus affecting male traits and the other affecting female traits. Further study in populations that have accumulated more recombination will be required to test this more fully. However, if genes with such effects exist, their evolutionary origins and effects would be of great interest. As an example, estrogen levels are known to have male- and female-specific effects on different features relating to muscle and neural function (GILLIES et al. 2004; GLENMARK et al. 2004). Therefore, genes affecting estrogen levels or the density of estrogen receptors in various organs could produce the observed pattern where QTL variants affect different traits in males and females.

Formal tests for pleiotropy (KNOTT and HALEY 2000; EHRICH et al. 2003) were performed but the method appeared to break down, especially when many traits had peak LPR scores within a few centimorgans. After the first set of tests was complete, no pleiotropic locus had >17 individual-trait QTL included in it, but there were a number of instances of loci that had highly overlapping or even identical confidence intervals and/or LPR peaks within 3 cM of each other. As the null hypothesis is pleiotropy, judgment was used on each chromosome as to whether pleiotropy could really be rejected. This resulted in a reduction from an initial 132 pleiotropic loci to the final 105. In most cases combining loci resulted in pleiotropic loci with very high numbers of traits, for instance, the creation of 8 loci with effects on 18 traits. One-LOD confidence intervals, traditional since the beginning of QTL analysis (OTT 1985; LANDER and BOTSTEIN 1989), are shown in Table 3. The utility of the measure, however, is questionable when the average pleiotropic LPR is 10.10. A possible alternative for QTL studies with high LPRs is a range based on the drop-off of a percentage of the total LPR. For example, if the percentage chosen was 20%, then a QTL with a peak LPR of 10 would include in the confidence interval positions surrounding the peak with LPR > 8.

Antagonistic pleiotropy for size, with a substantial and significant mix of positive and negative additive genotypic values, occurred in 13% of all pleiotropic loci. In these loci the LG/J allele results in some larger traits and some smaller traits. This is in contrast to earlier studies of the mandible (EHRICH et al. 2003) and the skull (LEAMY et al. 1999) in this population that found only two such loci. Further fine-mapping studies in later generations of the AIL formed from intercross II will help determine whether these pleiotropic relationships are further supported or resolved into closely linked loci.

The number of traits affected by a pleiotropic locus varied, from 11 loci affecting single traits to loci with effects on as many as 30 traits. We expect pleiotropic loci that affect a large number of traits to also affect one or both of the body-weight traits (week-10 body weight or weight at necropsy), as these loci may affect overall body size. Twenty-two percent of the pleiotropic QTL affected one or both of the weight traits. Loci with effects on body weight affected an average of 13.1 traits, while those loci that did not affect either body-weight trait had effects on an average of 6.0 traits. Thus the presence of a body-weight QTL frequently indicated a locus that influenced overall skeletal size as well. Pleiotropic loci affecting many traits and having high LPRs may include genes with strong impacts on whole skeletal development, such as those that encode certain hormones. For example, we would expect to detect a QTL at insulin-like growth factor 1 (Igf-1), given its known effects on skeletal growth (NIU and ROSEN 2005), and indeed it is located within the confidence interval of pleiotropic locus Skl10.03, which affects 14 traits and has an LPR of 9.00.

It is consistent with Chai's premolecular genetics work on body size (CHAI 1956a,b, 1957) and this group's work on body composition and a subset of skeletal-trait effects (CHEVERUD et al. 1996, 1997, 2001; KRAMER et al. 1998; VAUGHN et al. 1999; KENNEY-HUNT et al. 2006) that many loci with small, additive effects were identified. We expect that there are sizable epistatic effects as well, given that in studies of a more limited number of skeletal traits (femur, tibia, humerus, and ulna lengths), Cheverud and colleagues found extensive epistasis (PAVLICEV et al. 2007; NORGARD et al. 2008). While multiple individual-trait QTL may underlie the pleiotropic loci due to the level of resolution of an F₂ intercross study (KENNEY-HUNT et al. 2006; CHRISTIANS and SENGER 2007), pleiotropy was found to be widespread with most traits affected by multiple loci of small individual effect.

The extensive pleiotropy found here documents one way in which traits can be co-inherited. At the phenotypic level, selection for compatible trait values of functionally and developmentally related traits is predicted to cause their co-inheritance and hence their genetic and phenotypic correlation (OLSEN and MILLER 1958; LANDE 1980; CHEVERUD 1982, 1984). More recently, Cheverud and colleagues (CHEVERUD et al. 2004; PAVLICEV et al. 2007; WAGNER et al. 2007) have suggested that pleiotropic relationships should reflect the coselection of traits such that pleiotropic effects would be favored among traits selected together and not favored among traits selected independently. Our analysis of the relationship between pleiotropy and phenotypic correlation indicates that these two measures of trait relationship are relatively strongly correlated. Not surprisingly, traits that share pleiotropic effects at individual QTL tend to be phenotypically correlated. It is not possible to estimate genetic correlations in this F₂ intercross population due to the lack of family structure but the pleiotropic effects of QTL cause genetic correlation (CHEVERUD 1984) and genetic correlation makes up a substantial component of the phenotypic correlations measured here (LYNCH and WALSH 1998). Morphological evolution is facilitated when functionally and developmentally related traits are genetically correlated. Extensive pleiotropy of functionally or developmentally related characters has implications for artificial as well as natural selection. For example, pleiotropy in domesticated dogs (CHASE et al. 2002) may be responsible for the enormous and rapid diversification of dog breed phenotypes. Selection acting on a few loci could cause changes in many characters. Due to the similarity of phenotypic correlation and pleiotropic patterns, it appears that phenotypic correlations may be used to predict which traits will be pleiotropically linked.

The study presented here, with a refined genetic map and a large number of traits encompassing the whole skeleton, provides unprecedented detail about the genetic architecture of skeletal morphology and information about the role of genetic variation in skeletal evolution.

The authors are grateful to Ty T. Vaughn, Andrea Peripato, Kilinyaa Cothran, Christy Perel, Safina Koreishi, Robin Linsey, Eric Routman, and all the cheerful participants in weekly peeling parties for their contributions to the project. This work was funded by the Biotechnology and Biological Sciences Research Council (BBSRC) (J.B.W.), by an Underwood Fellowship from the BBSRC (J.M.C.), by National Institutes of Health grants DK055736 (J.M.C.) and AR053224 (J.M.C.), and by National Science Foundation doctoral dissertation improvement grant DEB-0413039 (J.K.H. and J.M.C.).

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